Question: Simplify the following expression and state the condition under which the simplification is valid. You can assume that $x \neq 0$. $q = \dfrac{5x(4x - 7)}{x} \div \dfrac{3(4x - 7)}{10} $
Explanation: Dividing by an expression is the same as multiplying by its inverse. $q = \dfrac{5x(4x - 7)}{x} \times \dfrac{10}{3(4x - 7)} $ When multiplying fractions, we multiply the numerators and the denominators. $q = \dfrac{ 5x(4x - 7) \times 10 } { x \times 3(4x - 7) } $ $ q = \dfrac{50x(4x - 7)}{3x(4x - 7)} $ We can cancel the $4x - 7$ so long as $4x - 7 \neq 0$ Therefore $x \neq \dfrac{7}{4}$ $q = \dfrac{50x \cancel{(4x - 7})}{3x \cancel{(4x - 7)}} = \dfrac{50x}{3x} = \dfrac{50}{3} $